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Let's say we have a page with the slug my-gallery-demo and in the content there is this shortcode like this one:

Let's say we have a page with the slug my-gallery-demo and in the content there is a shortcode like this one:

/*
* Get an array of the 'ids' parameter from the gallery shortcode that is placed in the content of a post/page with a given slug. 
* @param string $slug Post slug.  
* @param string $type Post type.  
* @return array Array of the gallery shortcode ids parameter.
*/
function get_gallery_ids_wpse_87978($slug,$type){
        $output=array();
        $my_query = new WP_Query(array('name'=>$slug,'post_type'=>$type));
        while ($my_query->have_posts()) : $my_query->the_post(); 
            $content=get_the_content();
            preg_match('/ids=\"([0-9,]+)\"/i', $content, $matches);
            if(isset($matches[1])){
                $output = explode(",",$matches[1]); // let's take the last set of ids
            }           
        endwhile;
        return $output;
}       

We have for example a page with the slug my-gallery-demo and in the content there is this shortcode like this one:

To display 4 random images from this shortcode we do the following:

// initial values:
$slug='my-gallery-demo'; // EDIT post/page slug that contains the gallery shortcode 
$type='page'; // EDIT post slug that contains the gallery shortcode 
$size='thumb'; // EDIT image size (thumb,large,full,...)
$n=4; // EDIT number of random images to show

// fetch all ids from the gallery shortcode:
$ids=get_gallery_ids_wpse_87978($slug,$type);

// get n random keys from the $ids array:
$random_ids=array_rand($ids,$n);

// display a list of n random images:
echo '<ul>';
foreach($random_ids as $random_id){
      echo '<li>';
      echo wp_get_attachment_image( $ids[$random_id], $size );
      echo '</li>';
 }
echo '</ul>';

/*
* Get an array of the gallery shortcode ids from a page content with a given slug 
* @param string $slug Post slug.  
* @param string $type Post type.  
* @return array Array of the exploded ids parameter.
*/
function get_gallery_ids_wpse_87978($slug,$type){
        $output=array();
        $my_query = new WP_Query(array('name'=>$slug,'post_type'=>$type));
        while ($my_query->have_posts()) : $my_query->the_post(); 
            $content=get_the_content();
            preg_match('/ids=\"([0-9,]+)\"/i', $content, $matches);
            if(isset($matches[1])){
                $output = explode(",",$matches[1]); // let's take the last set of ids
            }           
        endwhile;
        return $output;
}       

Let's say we have a page with the slug my-gallery-demo and in the content there is this shortcode like this one:

To display 4 random thumb images from this shortcode we do the following:

// initial values:
$slug='my-gallery-demo'; // EDIT post/page slug that contains the gallery shortcode 
$type='page'; // EDIT post type (post,page,...) 
$size='thumb'; // EDIT image size (thumb,large,full,...)
$n=4; // EDIT number of random images to show

// fetch all ids from the gallery shortcode:
$ids=get_gallery_ids_wpse_87978($slug,$type);

// get n random keys from the $ids array:
$random_ids=array_rand($ids,$n);

// display a list of n random images:
echo '<ul>';
foreach($random_ids as $random_id){
      echo '<li>';
      echo wp_get_attachment_image( $ids[$random_id], $size );
      echo '</li>';
 }
echo '</ul>';

/*
* Get an array of the 'ids' parameter from the gallery shortcode that is placed in the content of a post/page with a given slug. 
* @param string $slug Post slug.  
* @param string $type Post type.  
* @return array Array of the gallery shortcode ids parameter.
*/
function get_gallery_ids_wpse_87978($slug,$type){
        $output=array();
        $my_query = new WP_Query(array('name'=>$slug,'post_type'=>$type));
        while ($my_query->have_posts()) : $my_query->the_post(); 
            $content=get_the_content();
            preg_match('/ids=\"([0-9,]+)\"/i', $content, $matches);
            if(isset($matches[1])){
                $output = explode(",",$matches[1]);
            }           
        endwhile;
        return $output;
}       

Usage example:

/*
* Get an array of the 'ids' parameter from the gallery shortcode that is placed in the content of a post/page with a given slug. 
* @param string $slug Post slug.  
* @param string $type Post type.  
* @return array Array of the gallery shortcode ids parameter.
*/
function get_gallery_ids_wpse_87978($slug,$type){
        $output=array();
        $my_query = new WP_Query(array('name'=>$slug,'post_type'=>$type));
        while ($my_query->have_posts()) : $my_query->the_post(); 
            $content=get_the_content();
            preg_match('/ids=\"([0-9,]+)\"/i', $content, $matches);
            if(isset($matches[1])){
                $output = explode(",",$matches[1]); // let's take the last set of ids
            }           
        endwhile;
        return $output;
}       

Usage example:

We have for example a page with the slug my-gallery-demo and in the content there is this shortcode like this one:

[gallery ids="1376,1375,341,213,211,210,209,208,206,205"]

To display 4 random images from this shortcode we do the following: